Rietveld Quantitative Phase Analysis of OPC Clinkers, Cements and Hydration Products

5 Reviews in Mineralogy & Geochemistry Vol. 74 pp. 169-209, 2012 Copyright © Mineralogical Society of America 1529-6466/12/0074-0005$05.00 DOI: 10.2138/rmg.2012.74.5 Rietveld Quantitative Phase Analysis of OPC Clinkers, Cements and Hydration Products Miguel A. G. Aranda,* Ángeles G. De la Torre Departamento de Química Inorgánica, Cristalografía y Mineralogía Universidad de Málaga 29071 Málaga, Spain email: [email protected] Laura León-Reina Servicios Centrales de Investigación Universidad de Málaga 29071 Málaga, Spain BRIEF INTRODUCTION It has been more than twenty years since the excellent volume of Reviews in Mineralogy dedicated to Modern Powder Diffraction was published (Bish and Post 1989). That volume contained a series of key articles ranging from the basic of powder diffraction to sample preparation and synchrotron and neutron powder diffraction. Within that volume, quantitative phase analysis was extensively discussed in a specific chapter (Snyder and Bish 1989). Snyder and Bish (1989) discussed the Reference Intensity Ratio approach (also known as Chung method), the method of standard additions (also known as spiking method) and the full patternfitting approach using both the Rietveld method and the observed patterns method. The reader is referred to that volume for the basics of powder diffraction, and to the specific chapter by Snyder and Bish (1989) for the history of quantitative phase analysis from powder diffraction and for a discussion or the early findings. Quantitative phase analysis by X-ray powder diffraction dates back to 1925 (Navias 1925). In this work, the amount of mullite obtained by firing selected clays (and a feldspar) was determined by the direct comparison of the intensities of two diffraction lines of the fired samples with those of pure mullite. The patterns were recorded on photographic negatives after an X-ray exposure of 165 hours (almost a week). Quantitative phase analysis (QPA) from diffraction data can be obtained from a number of methods explained in classical books (Klug and Alexander 1974; Cullity 1978; Snyder and Bish 1989; Zevin and Kimmel 1995; Jenkins and Snyder 1996). However, it is now safe to say that QPA from powder diffraction data is nowadays mainly based on the Rietveld methodology (Rietveld 1969; Hill and Howard 1987; Bish and Howard 1988; Bish and Post 1993; Madsen and Scarlett 2008). Hence, the term Rietveld quantitative phase analysis (RQPA) has been coined. The advantages of using a full pattern-fitting over single peak(s) approaches are discussed in those papers and they will not be further addressed here. Hence, we will focus on RQPA. The readers should also be aware of two excellent articles which were the outcome of a round robin study on quantitative phase analysis by powder diffraction mainly using the Rietveld method (Madsen et al. 2001; Scarlett et al. 2002). These interlaboratory comparison studies made some indispensable recommendations for carrying out an accurate RQPA and included results concerning the influence of sample-related effects such as preferred orientation and microabsorption. However, it is also worth mentioning, that the key book entitled “The Rietveld Method” (Young 1993) does not contain a chapter on quantitative phase 170 Aranda, De la Torre, León-Reina analysis. Furthermore, the key paper “Rietveld refinement guidelines” (McCusker et al. 1999), supported by the International Union of Crystallography, did not dedicate a section to RQPA. On the other hand, building materials, such as ordinary Portland cements (OPCs), are very complex samples of worldwide importance, hence quantitative knowledge of their mineralogical composition is necessary to predict performances (Taylor 1997). Ultimately, the assemblage of crystalline phases, and not the bulk chemistry, determines cement features. In fact, the hydraulic properties of a mortar/concrete mainly depend on the cement mineralogical composition and its texture (Bentz 2008; Skibsted and Hall 2008; Scrivener and Nonat 2011). The most widely used method of estimating the potential phase composition of Portland cement in cement plants is the Bogue calculation from its elemental analysis usually determined by X-Ray Fluorescence, XRF (Bogue 1929; Taylor 1989). However, it is well known that the phase abundance calculated by this indirect approach may be quite far from the true values. This is due mainly to three reasons: i) the four main clinker phases are solid solutions with compositions significantly different from the stoichiometric pure-phases; ii) there is no certainty of attaining equilibrium conditions (both in the kiln and for sure in the cooling process, Hong et al. 2001); iii) the presence of minor phases. As an alternative approach, RQPA allows a direct measurement of the phase content of cements. So, on-line systems for RQPA of clinkers and cements are becoming widespread. However, we will not deal here with on-line RQPA at cement plants. The reader is addressed to specific publications dealing with this subject including reproducible sample preparation, fast data acquisition and fast-and-robust data analysis (Moller 1998; Manias et al. 2001; Scarlett et al. 2001; Fullmann and Walenta 2003; Paul et al. 2004; Enders and Berger 2007; De la Torre et al. 2011). Therefore, this review focuses on the use of RQPA for understanding OPC clinkers, cements and pastes, at central laboratories. It must be highlighted that a very recent review article has been dedicated to the application of the Rietveld method to the analysis of anhydrous cements (Le Saout et al. 2011). Furthermore, a second broad article dealing with direct determination of phases in OPCs by quantitative X-ray powder diffraction has also been reported (Stutzman 2011). Hereafter, cement nomenclature will be used, i.e., C = CaO, S = SiO2, A = Al2O3, F = Fe2O3, M = MgO, S = SO3, C = CO2, H = H2O, K = K2O and N = Na2O. Hence, typical cement phase such as alite (Ca3SiO5), belite (Ca2SiO4), tricalcium aluminate (Ca3Al2O6), calcium aluminoferrate (Ca4Al2Fe2O10), gypsum (Ca2SO4·2H2O) or calcite (CaCO3) are abbreviated as C3S, C2S, C3A, C4AF, CSH2 and CC, respectively. Most cement compounds are not pure stoichiometric phases but they may incorporate many ions as extensively discussed (Taylor 1997; Le Saout et al. 2011). In addition, AFm and AFt set of phases should be defined. AFm stands for the abbreviation for “alumina, ferric oxide, mono-sulfate” or “Al2O3-Fe2O3-mono”, in the same way AFt stands for a similar abbreviation but “tri-sulfate” or “Al2O3-Fe2O3-tri”. The AFm phase refers to a family of hydrated calcium aluminates based on the hydrocalumite structure, Ca4Al2(OH)12·[Cl(OH)]·6H2O. The archetype AFm phase is C3A·CaSO4·12H2O or Ca4Al2(OH)12·[SO4]·6H2O, known as Kuzelite, but Al can be partly replaced by Fe and SO42− can be partly or fully replaced by OH−, CO32− and other anions (Pollmann 2006, Matschei et al. 2007a). The different hydration stages strongly influence the X-ray powder diffraction patterns (Pollmann 2007; Balonis and Glasser, 2009). By far the most common AFt phase is ettringite which has the following stoichiometry C3A·3CaSO4·32H2O that can also be written as Ca6Al2(SO4)3(OH)12·26H2O. THE RIETVELD METHOD Crystalline compounds have long range periodic order and its interaction with X-rays (or neutrons) yield powder diffraction patterns plenty of peaks/reflections. The position, height and even width of these reflections may be used to determine many aspects of the sample structure/ Rietveld Quantitative Phase Analysis of OPC 171 microstructure. The reader is referred to the two most recent books in “Powder Diffraction” to expand on that (Pecharsky and Zavalij 2005; Dinnebier and Billinge 2008). The Rietveld method is a technique devised by Hugo Rietveld in the late sixties (Rietveld 1967, 1969) for a deeper characterization of polycrystalline compounds by treating in a “better/different” way the powder diffraction patterns. The very original contribution of the Rietveld method to powder diffraction was its conceptual breakthrough: “To use measured powder pattern intensities instead of reflection (peak) intensities.” This conceptual breakthrough, together with the coming of computers, allowed to properly dealing with strongly overlapping reflections. The introduction of this technique was a significant step forward in the diffraction analysis of crystalline powder samples. The powder diffraction analysis at that moment worked with extracted reflection intensities which was a very serious difficulty in the case of overlapping reflections. The Rietveld (whole-profile) method uses a least squares approach to optimize a theoretical line profile until it matches in the best possible way the measured sample powder diffraction profile (see Eqn. 1); where Sy is the function to be minimized, wi is the statistical weight, and yi(obs) and yi(cal) are the observed and calculated powder diffraction intensities for the i-point of the powder pattern, respectively. = − ∑2 (obs) (cal) (1) y ii i i S wy y The calculated intensity, yi(cal), for each point of the powder pattern, 2qi, is obtained as the sum of the contribution of all reflections (k) which give intensity to that i-point above the background, yb(2qi), see Equation (2): a = q + q− q q ∑2 (cal) (2 ) (2 2 ) (2 ) (2) i b i kk i k i k k y y S m F h Lp P where Sa is the scale factor for the pure crystalline a-phase to be studied, k stands for the reflections which contribute to that point of the pattern, mk is the multiplicity of that reflection, Fk is the structure factor of that reflection, h(2qi−2qk) is the function that distributes the intensity of that reflection in a given 2q range, Lp(2qi) stands for the Lorentz and polarization correction, and Pk stands for additional corrections that may be needed (preferred orientation, extinction, etc.). Equation (2) may be extended to a sample containing m-crystalline phases, see Equation (3), by summing up the contribution of every crystalline phase. = = q + q− q q ∑∑ 2 1 (cal) (2 ) (2 2 ) (2 ) (3) m i b i i kk i k i k ik y y S m F h Lp P The Rietveld method was originally devised for the refinement of crystal and magnetic structures from powder neutron data. However, today the uses of the Rietveld method are numerous and help extracting the maximum information already present in a powder diffraction pattern. This information is listed just below and it must be highlighted that the Rietveld method is making a profound impact in every listed use as it increases the accuracy and precision of the extracted results. It can also be said that Hugo Rietveld did not envisage some of these uses including quantitative phase analysis (Rietveld 2010). From the position of the diffraction peaks: i) lattice parameters, ii) space group determination, iii) qualitative phase analysis (phase identification), and iv) macro-strain; from the intensities of the diffraction peaks: v) crystal (nuclear) structure (including atomic positions, occupation factors and atomic displacement parameters), vi) magnetic structure, vii) texture (preferred orientation), and viii) quantitative phase analysis; from the widths/shapes of the diffraction peaks: ix) micro-strains (mainly in solid solutions), and x) coherent diffraction domain size(s). 172 Aranda, De la Torre, León-Reina In this review article, we will focus on the viiith-application, quantitative phase analysis. We address the reader to some selected books and papers for a deeper insight of the role of the Rietveld method in the remaining applications (Young 1993; McCusker et al. 1999; David et al. 2002; Shin et al. 2002; Fitzpatrick and Lodini 2003; Balzar et al. 2004; Pecharsky and Zavalij 2005; Kaduk 2007a,b; Dinnebier and Billinge 2008; David and Shankland 2008; Soleimanian and Aghdaee 2008; Markvardsen et al. 2008). Finally, new ways of learning are being explored. In addition to books, papers and training in laboratories with proven experience, other methods are emerging. If the reader is keen of using internet-distributed audio/visual material, then the following references are a good starting point (Toby 2007, 2010). General issues For a successful Rietveld quantitative phase analysis, several steps have to be fulfilled. Initially, sample has to be properly prepared and this will depend upon the nature of the sample itself and the diffractometer where the data will be taken. This will be briefly discussed in a later section. Secondly, the diffractometer should be well aligned and maintained. Different optical configurations are possible in modern diffractometers and the optimal set-up should be used. Under these two pre-requisites, a good powder diffraction pattern may be taken and RQPA can be carried out. It must be highlighted that the results of any analysis cannot be better than the raw data. Therefore, a lot of care is needed in these two initial steps in order not to spend/waste a lot of time in data analysis/evaluation without conclusive results. Once good powder diffraction data have been taken, a third step follows: qualitative phase analysis. Every crystalline phase in the sample should be identified. This is easy to say but sometimes quite complex to fulfill. The strong peak overlapping in the diffraction patterns does not allow to conclusively determining all phases present in some cases. Then a possible strategy follows, we compute the RQPA with the phases which are clearly present in the pattern and, from the net intensity in the difference curve, the remaining low-content phases are determined. Alternatively, a trial-and-error method can be used. In addition to the main, clearly-observed phases, dubious phases are added to the Rietveld calculation and its absence/ presence can be individually estimated. In any case, when the main (all) phases are identified, the fourth step is to carry out the RQPA with the appropriate software. A full list, and discussion, of the programs available for this task is out of the scope of this paper. However, we can suggest the ccp14 web site for a list of Rietveld programs (http://www.ccp14.ac.uk/solution/rietveld_software/index.html) and mention that GSAS (Larson and von Dreele 1994; Toby 2001) and FULLPROF (RodriguezCarvajal 1993; Roisnel and Rodriguez-Carvajal 2001) are the widest used packages. Many other packages can also be used for RQPA and we underline just a few: BGMN, SIROQUANT, TOPAS and HighScore Plus. In any case, in addition to the raw data, any Rietveld program needs a control file to execute the refinements. In this control file, the crystal structures of the different components must be included. The fit is carried out by optimizing all appropriate variables such as: i) scale factor of every crystalline phase; ii) background parameters for the chosen function; iii) unit cell parameters for every crystalline phase; iv) peak shape parameters for every computed phase; and finally, v) correction parameters which may be phase-dependent (such as preferred orientation, extinction, etc.) or pattern-dependent (zero-shift, absorption correction when working in transmission geometry, etc.). Usually, for RQPA the structural descriptions (atomic positional parameters, atomic displacement parameters and occupation factors) are not optimized but kept as reported in the structural studies. The RQPA method does not require calibration curve or internal standard. However, the crystal structures of all crystalline constituents must be known. This is a prerequisite as the process consists of the comparison between the measured and the calculated patterns (the calculated pattern being computed from the crystal structures). Rietveld Quantitative Phase Analysis of OPC 173 The application of RQPA to clinkers/cements/pastes is not straightforward for the following reasons: i) there are many phases, usually more than five, which increases the diffraction peak overlapping and so the correlations; ii) each phase has its own mass absorption coefficient which may yield the microabsorption problem (see below); iii) the small mean penetration depth of X-rays (~30 mm for Cu Ka, 1.54 Å) implies that only a thin layer is analyzed in the Bragg-Brentano q/2q geometry which may lead to poor particle statistics; iv) some phases, for instance alite or gypsum crystallize as plaques which show preferred orientation and so increases the errors; v) phases can crystallize as several polymorphs that must be identified a priori; vi) the diffraction peak broadening for some phases may be anisotropic and it must be properly model; and vii) the atomic impurities inside each phase are not known and their scale factors are computed for ideal/stoichiometric phases. In any case, this method has several advantages over other methods based on powder diffraction and other technologies (microscopy, thermal analysis, etc.). A comparison between RQPA results and those obtained with alternative/complementary technologies will be given below. The direct output of the RQPA is a set of scale factors, one for every crystalline phase within the mixture with computed crystal structures. In addition, several other parameters may be of interest: i) unit cell parameters (to have an idea of the existence of solid solutions); ii) preferred orientation of some phases (to have an insight of the particle shapes of these phases); iii) peak shape widths to know about the microstructures. The key transformation of the phase scale factors to phase contents is discussed in a section below. However, it must be highlighted that the best available structural description should be used in order to extract the best possible scale factor value for every phase. This is evaluated by the flatness of the difference curve and also by obtaining low Rietveld-disagreement indices (R-factors). However, the lowest R-factors may also be obtained for wrong analysis. So, it is important to optimize those parameters that allow their minimization without excessive correlations. It is also important to understand the definitions for R-factors which are discussed in standard papers (Young 1993; McCusker et al. 1999). However, a much personal view has been reported (Toby 2006) which was mainly dedicated to the refinement of crystal structures but some concerns and discussions are of overall interest. Structural description of the phases present in OPC materials The main clinker phases are alite, belite and aluminate in white Portland clinkers and also ferrite in grey Portland clinkers. In addition several other minor phases may be present: lime, periclase, arcanite, aphthitalite and others, see Table 1. An excellent review about the phases present in OPC clinkers has been very recently published (Le Saout et al. 2011). We want to draw the attention that several issues are discussed in that paper including the selection of the alite polymorph, the implications of the Fe/Al ratio in ferrite quantification, and the consequences of the solid solution existence in most clinker phases (small change in the structure factors and densities of the analyzed phases). Portland cements are fabricated by adding a setting regulator to the clinker. The sulfate phases added for this purpose may be gypsum (CaSO4·2H2O), hemihydrate (CaSO4·½H2O) also known as bassanite or anhydrite (CaSO4). Different Portland cements may have different additions, for instance calcite (CaCO3) or quartz (SiO2). Additionally, other highly-amorphous materials may be added for blended cement and concrete production such as blast furnace slag (BFS), pulverized fly ash (PFA) or pozzonale minerals. It must be kept in mind that these additions also contain some crystalline phases (for instance mullite or hematite) that must be quantified in blended cements. Table 2 gives a list of additional phases that may be present in (blended) OPC cements. New phases appear during hydration of OPC cements. Table 3 lists additional (hydrated) phases that may be present in Portland cement pastes. It should be noted that a review of 174 Aranda, De la Torre, León-Reina Table 1. Structural details for phases that may be present in OPC clinkers. Phase Formula Crystal system/ notation m (cm−1)ICSD codes PDF codes Ref# Alite Ca3SiO5-Mg,Al Monoclinic/M3310.4 94742 01-070-8632 [1] Ca3SiO5-Mg Triclinic/T3308.5 162744 [2] Ca3SiO5Triclinic/T1304.6 4331 01-070-1846 [3] Belite Ca2SiO4Monoclinic/b299.9 81096 01-086-0398 [4] Ca2SiO4Orthorhombic/a′ 298.1 81097 01-086-0399 [4] Ca2SiO4Orthorhombic/g268.2 81095 01-086-0397 [4] Aluminate Ca3Al2O6Cubic 277.1 1841 01-070-0839 [5] Ca8.5NaAl6O18 Orthorhombic 278.9 100220 01-083-1359 [6] Ca8.25Na1.5Al6O18 Monoclinic 246.5 100221 01-083-1360 [6] Ferrite Ca2AlFeO5Orthorhombic 502.8 9197 01-071-0667 [7] Lime CaO Cubic 401.2 52783 01-071-4121 [8] Periclase MgO Cubic 99.5 9863 01-071-1176 [9] Arcanite K2SO4Orthorhombic 219.9 79777 01-083-0681 [10] Aphthitalite K3Na(SO4)2Rhombohedral 195.4 26018 01-074-0398 [11] Thenardite Na2SO4Orthorhombic 73.0 81506 00-037-1465 [12] Ca-Langbenite Ca2K2(SO4)3Orthorhombic 209.1 040989 01-074-0404 [13] Sulfate-spurrite Ca5(SiO4)2(SO4) Orthorhombic 255.6 085123 01-088-0812 [14] Ellesteadite Ca10(SiO4)3(SO4)3Cl2Hexagonal 272.7 154205 00-041-0479 [15] Fluorellesteadite Ca10(SiO4)3(SO4)3F2Hexagonal 261.8 97203 01-072-7301 [16] Mayenite Ca12Al14O33 Cubic 198.6 241243 70-2144 [17] # References: [1] De la Torre et al. 2002; [2] De la Torre et al. 2008; [3] Golovastikov et al. 1975; [4] Mumme et al. 1995; [5] Mondal and Jeffry 1975; [6] Takeuchi et al. 1980; [7] Colville and Geller 1971; [8] Smith and Leider 1968; [9] Sasaki et al. 1979; [10] Ojima et al. 1995; [11] Okada and Ossaka 1980; [12] Rasmussen et al. 1996; [13] Speer and Salje 1986; [14] Irran et al. 1997; [15] Saint-Jean and Hansen 2005; [16] Pajares et al. 2002; [17] Palacios et al. 2007. Rietveld Quantitative Phase Analysis of OPC 175 Table 2. Structural details for additional phases that may be present in OPC (blended) cements. Phase Formula Crystal system/ notation m (cm−1)ICSD codes PDF codes Ref# Gypsum CaSO4.2H2O Monoclinic 141.0 151692 33-0311 [1] Hemihydrate CaSO4.0.5H2O Monoclinic 193.4 79528 01-083-0438 [2] Anhydrite-III CaSO4Hexagonal 188.7 24473 01-073-1942 [3] Anhydrite-II CaSO4Orthorhombic 220.1 16382 01-072-0916 [4] Syngenite K2Ca(SO4)2.H2O Monoclinic 194.3 157072 28-0739 [5] Calcite CaCO3Rhombohedral 193.8 80869 01-086-0174 [6] Dolomite CaMg(CO3)2Rhombohedral 134.7 31277 01-075-1711 [7] Quartz SiO2Rhombohedral 92.3 41414 46-1045 [8] Gehlenite Ca2Al2SiO7Tetragonal 205.9 87144 01-089-5917 [9] Yeelemite Ca4Al6SO16 Orthorhombic 169.9 80361 42-1478 [10] Ca4Al6SO16 Cubic 169.9 9560 01-071-0969 [11] Mullite Al4SiO8Orthorhombic 99.5 23867 01-073-1389 [12] Yoshiokaite Ca5.5Al11Si5O32 Rhombohedral 153.8 69380 01-080-1547 [13] Hematite Fe2O3Rhombohedral 1163.5 82904 01-087-1166 [14] Magnetite Fe3O4Cubic 1183.4 49549 01-077-1545 [15] Wollastonite CaSiO3Monoclinic 222.4 30884 00-043-1460 [16] Rankinite Ca3Si2O7Monoclinic 253.5 2282 01-070-1138 [17] Merwinite Ca3Mg(SiO4)2Monoclinic 258.3 43078 01-089-2432 [18] Akermanite Ca2Mg(Si2O7) Tetragonal 203.0 158177 00-035-0592 [19] Monticellite CaMg(SiO4) Orthorhombic 193.8 34591 00-035-0590 [20] # References: [1] De la Torre et al. 2004; [2] Bezou et al. 1995; [3] Floerke 1952; [4] Kirfel and Will 1980; [5] Ballirano et al. 2005; [6] Maslen et al. 1995; [7] Effenberger et al. 1983a; [8] Will et al. 1988; [9] Louisnathan 1971; [10] Calos et al. 1995; [11] Saalfeld and Depmeier 1972; [12] Sadanaga et al. 1962; [13] Steele and Pluth 1990; [14] Sawada 1996; [15] Fleet 1984; [16] Hesse 1984; [17] Saburi et al. 1976; [18] Yamaguchi and Suzuki 1967; [19] Gemmi et al. 2007; [20] Onken 1965. 176 Aranda, De la Torre, León-Reina Table 3. Structural details for additional phases that may be present in OPC hydration products. Phase Formula Crystal system/ notation m (cm-1)ICSD codes PDF codes Ref# Portlandite Ca(OH)2Rhombohedral 211.4 15471 01-072-0156 [1] Gibbsite Al(OH)3Monoclinic 57.1 6162 01-070-2038 [2] Tobermorite Ca5Si6O16(OH)2·7H2O Monoclinic 145.0 152489 00-029-0331 [3] Jennite Ca9Si6O18(OH)6·8H2O Triclinic 164.3 151413 00-018-1206 [4] Hydrogarnet or C3AH6Ca3Al2(OH)12 Cubic 163.7 202316 01-084-1354 [5] Katoite Ca3Al2(OH)7.6(SiO4)1.1 Cubic 185.5 172077 00-038-0368 [6] AFt Ettringite Ca6Al2(OH)12(SO4)3·26H2O Rhombohedral 84.4 155395 00-041-1451 [7] Ettr-CO3Ca6Al2(OH)12(CO3)3·26H2OStructure not reported 00-036-1465 Thaumasite Ca6Si2(OH)12(CO3)2(SO4)2·24H2O Hexagonal 85.7 31247 01-075-1688 [8] AFm Kuzelite or C4A S H12 Ca4Al2(OH)12[SO4]·6H2O Rhombohedral 115.8 100138 01-083-1289 [9] Friedel’s salt Ca4Al2(OH)12[Cl]2·4H2O Rhombohedral 146.7 88617 01-089-8294 [10, 11] Kuzel’s salt Ca4Al2(OH)12[(SO4)0.5Cl]·5H2O Rhombohedral 124.0 00-019-0203 [12] Monocarbo-aluminate Ca4Al2(OH)12[CO3]·5H2O Triclinic 124.7 59327 01-087-0493 [13] Hydrocalumite Ca4Al2(OH)12[Cl(CO3)0.5]·4.8H2O Monoclinic 130.1 63250 01-078-2050 [14] Hemicarbo-aluminate Ca4Al2(OH)12[OH(CO3)0.5]·5.5H2OStructure not reported 00-041-0221 C2AH8Ca4Al2(OH)12[Al(OH)4]2·6H2OStructure not reported 00-011-0205 Strätlingite or C2ASH8Ca4Al2(OH)12[AlSi(OH)8]2·2H2O (Gehlenite hydrate) Rhombohedral 98.8 69413 01-080-1579 [15] # References: [1] Petch 1961; [2] Saalfeld and Wedde 1974; [3] Bonaccorsi et al. 2005; [4] Bonaccorsi et al. 2004; [5] Lager et al. 1987; [6] Ferro et al. 2003; [7] Goetz-Neunhoeffer and Neubauer 2006; [8] Effenberger et al. 1983b; [9] Allmann 1977; [10] Renaudin et al. 1999; [11] Rousselot et al. 2002; [12] Mesbah et al. 2011; [13] François et al. 1998; [14] Sacerdoti and Passaglia 1988; [15] Rinaldi et al. 1990. Rietveld Quantitative Phase Analysis of OPC 177 calcium silicate hydrates has been reported (Richardson 2008). Furthermore, the reader is also referred to an excellent review dealing with the density of cement phases including those of AFm and other hydrates (Balonis and Glasser 2009). The mineralogy (phases) of the hydrates compounds may depend upon the additions in blended cements (Matschei and Glasser 2010) and this should be taken into account. Whole-pattern quantitative phase analysis approaches As stated above, conventional RQPA requires all crystal structures to be known. There are alternative whole-pattern quantitative phase analysis methods for crystalline phases with unknown structures (Smith et al. 1987; Taylor and Zhu 1992; Scarlett and Madsen 2006) however these approaches will not be discussed/reviewed here. The output of a RQPA study is a set of m-crystalline phase scale factors, ΣmSa, for a sample with m-crystalline phases. A phase scale factor, Sa, is related to the phase weight content, Wa, by Equation (4) (Hill and Howard 1987; Bish and Howard 1988) 2 K (4) e s W SV a a aa  = rm  where Ke is a constant which depends on the diffractometer operation conditions, ra is the crystallographic density of the a-phase, Va is the unit cell volume of a-phase, and ms is the sample mass absorption coefficient. Equation (4) can be rewritten as given in Equation (5): K (5) () e s W SZMV a a a  = m  where instead of using ra, the relation between Sa and Wa is based on the “ZMV” term with Z being the number of chemical units/formulas within the unit cell, M being the molecular mass of the chemical formula, and V the unit cell volume. Once the crystal structure is known, the “ZMV” term is known. In any case, the parameter to be extracted, Wa, depends on the phase scale factor, Sa, but also on Ke and ms. Unfortunately, these two variables are not known and they cannot be derived from the powder diffraction pattern of the sample under study. Currently, there are three main ways to derive the phase content, Wa, from the Rietveld refined scale factor, Sa. These three methods are based on different mathematical approaches and they have different experimental complexities. They will be treated in detail just below. I) Normalization to full crystalline phase content method. The simplest approach is the approximation that the sample is composed only of crystalline phases with known structures. These crystal structures are incorporated into the control file, and it was already shown (Hill and Howard 1987) that the weight fraction of a-phase, for a m-crystalline phase mixture, may be given by Equation (6): 1 () (6) () m ii i S ZMV W S ZMV aa a = =∑ The use of Equation (6) in RQPA eliminates the need to measure the instrument calibration constant, Ke, and the sample mass absorption coefficient, ms. However, the method normalizes the sum of the analyzed weight fractions to 1.0. Thus, if the sample contains amorphous phases, and/or some amounts of unaccounted for crystalline phases, the analyzed weight fractions will be overestimated. This approach is by far the most widely used method in RQPA and also in RQPA of OPCs. However, it must be highlighted that the resulting weight fractions are only accurate if the 184 Aranda, De la Torre, León-Reina C 3 S 2 C 3 S 1 y 7.4 7.6 7.8 8.0 8.2 8.4 8.6 8.8 C 3 S 1 NaK 3 (SO 4 ) 2 C 2 S C 4 AF C 4 AF C 3 A C 3 S 2 C 3 S 1 C 3 S 2 C 2 S NaK 3 (SO 4 ) 2 C 3 S 1 C 3 S 2 29.0 30.0 31.0 32.0 33.0 34.0 35.0 C 3 S 1 NaK 3 (SO 4 ) 2 C 2 S C 4 AF C 4 AF C 3 A C 3 S 2 C 3 S 1 C 3 S 2 C 2 S NaK 3 (SO 4 ) 2 C 3 S 2 C 3 S 1 C 3 S 1 C 3 S 2 C 3 S 1 y 29.0 30.0 31.0 32.0 33.0 34.0 35.0 C 3 S NaK 3 (SO 4 ) 2 C 2 S C 4 AF C 4 AF C 3 A C 3 S C 2 S NaK 3 (SO 4 ) 2 C 3 S C 3 S C 3 S º/2  = 0.40 Å (synchrotron data) = CuK 1 = CuK 1,2 C 3 S 1 I (a.u) I (a.u) I (a.u) Figure 4. Selected region of the Rietveld plots for the same commercial Portland clinker. Data were collected at: ID31 diffractometer of ESRF synchrotron (top), a laboratory diffractometer with a Ge(111) primary monochromator (middle), and a laboratory diffractometer with a graphite secondary monochromator (bottom). Note the similar resolution of synchrotron and CuKa1 patterns (modified after De la Torre et al. 2006). Rietveld Quantitative Phase Analysis of OPC 185 using these special raw meals (Chen and Juenger 2009a,b). However, it is now recognized that these materials (blast furnace slag or fly ash) are more eco-friendly as additions to ordinary Portland clinkers to produce blended cements in Europe or directly in the fabrication of concretes (North America). Therefore, the use of RQPA for studying these additions will treat in the next section dedicated to OPC cements. Another general use of RQPA is to study the role of mineralizing/flux agents in the kiln or the processing of industrial wastes in the kilns by analyzing the resulting clinker phase assemblage. As it has been described (Herfort et al. 2010), the mechanism of action of the trace elements incorporated into the clinker can be divided in two main steps depending on the amount of these elements: i) at low concentration, trace elements enter into the structure of the initial phases of the clinker as solid solutions (C3Sss, C2Sss, C3Ass, C4AFss); ii) at higher concentrations, the presence of new phases may be detected and quantified (Gineys et al. 2011). RQPA may help in both cases, initially by following the unit cell variations of the solid solution(s) and secondly, by quantification of the new phases. The implications of processing industrial waste(s) in the Portland kilns have been studied by RQPA. For instance, this approach has been used to evaluate the effects of chromium and nickel additions to Portland clinker raw meals. The final goal was to better characterize the processing of galvanic sludge which is the main hazardous solid waste produced by some metallurgical industries. A small decrease in the C3S contents were measured as the amount of Ni and Cr in the raw meals increases (Ferreira et al. 2008). For the production of Portland clinkers, mineralizers and/or fluxes are added to the raw mixes to accelerate reactions and enhance burnability. The traditional fluxes (Fe2O3 and Al2O3) may be partially substituted by the mineralizing pair CaF2/CaSO4 to produce clinkers with low aluminate contents at temperatures close 1400 °C. This is particularly useful for manufacturing white Portland clinkers because of the potential for energy conservation and seawater resistance. However, new phases may appear and in order to carry out RQPA, the crystal structures must be known. A work (Pajares et al. 2002) identified fluorellestadite in the mineralized white Portland clinker. Its crystal structure was determined and a satisfactory RQPA of the mineralized white Portland clinker was obtained. Figure 5 displays the Rietveld plot of this mineralized white Portland clinker, and a similar Rietveld plot for an ordinary white Portland clinker is also given for the sake of comparison. Cements RQPA in OPC cements can be used for a number of applications including: i) quantification of the crystalline phases in OPCs, including the ACn content if needed; ii) to analyze the amount and role of sulfate-containing phases; iii) to study the mineralogical phase assemblage in the materials used as addition(s), including their ACn contents; iv) to quantify all phases in blended OPC cements. The overall amorphous content has been studied in OPC clinkers as previously discussed. This type of study has also been carried out in cements and a thorough study by the external standard method (Jansen et al. 2011a) concluded that no significant amorphous content could be proven in that particular analyzed OPC cement. Commercial OPCs contain sulfate carriers in variable amounts. Gypsum (or other calcium sulfates) is added to the clinker during the milling process, where it may partially dehydrates to bassanite or even to soluble anhydrite-III. Due to different hydration kinetics of these phases, it is necessary to characterize the mineralogical composition of sulfate in a cement system in order to reach an optimal and reproducible setting and cement hydration (Seufert et al. 2009a). The formations and transformations of the five different phases in the CaSO4-H2O system have been studied in detail (Christensen et al. 2008). The use of RQPA for determining the amounts of gypsum, bassanite and anhydrite in OPC was already demonstrated several years ago (Fullmann and Walenta 2003; Walenta and Fullmann 2004; Seufert et al. 2009b). The 186 Aranda, De la Torre, León-Reina mineralogy of the sulfate source is very important for the fluidity, setting and hydration of mortars and concretes (Tang and Gartner 1988; Rossler et al. 2008). This technique has been very recently used for quantitative determination of the hydration products formed within minutes of mixing (e.g., ettringite, syngenite and secondary gypsum), to help identify the cause(s) of early stiffening (Ramlochan and Hooton 2011). Today supplementary cementitious materials (SCMs) are widely used in concrete either in blended cements or added separately in the concrete mixer. The use of silica rich materials influences the amount and kind of hydrates formed and thus the volume, the porosity and finally the durability of these materials (Lothenbach et al. 2011). Therefore, it is easy to understand that the mineralogical phase assemblage in different common additions has been deeply studied including PFA, bottom ash, metakaolin and BFS (Kumar et al. 2008; Korpa et al. 2009; Gonçalves et al. 2009; De Weerdt et al. 2011; Narmluk and Nawa 2011). Furthermore, RQPA has also been used to characterize other less common additions such as drinking water treatment plant sludge (Husillos-Rodriguez et al. 2010) or natural zeolites (Snellings et al. 2010). Table 4 reports a RQPA study of a fly ash carried out in our laboratory by the internal standard method described above. Figure 6 (top) shows the Rietveld plot for 2-Theta, deg Counts 28.0 29.0 30.0 31.0 32.0 33.0 34.0 35.0 X10E3 .0 2.0 4.0 C 3 S C 3 S C 3 S C 3 S C 3 S C 2 S C 2 S C 3 A C 2 S X10E3 .0 1.0 2.0 3.0 C 3 S C3S C 3 S C 3 S C 3 S C 2 S FLELL C 2 S, FLELL FLELL FLELL C 11 A 7. CaF 2 Figure 5. (top) Selected region of a Rietveld plot (CuKa1,2) for a mineralized white Portland clinker. (bottom) Selected region of the Rietveld plot for an ordinary commercial white Portland clinker. The main peaks are labeled and FLELL stands for fluorellestadite (modified after Pajares et al. 2002). Rietveld Quantitative Phase Analysis of OPC 187 this type of analysis with the main peaks labeled. An overall ACn content of ~75 wt% was obtained with mullite and quartz being the main crystalline phases (see Table 4). Finally, the analysis of blended cements containing BFS and PFA additions by RQPA (with internal standard) was already reported several years ago (Westphal et al. 2002; Walenta Fullmann and 2004). Many more studies have been reported in this subject mainly linked to the hydration characterization. Hence, some of these papers will be discussed in the next subsection. As an example of this type of analysis, Figure 6 (bottom) shows the Rietveld plot of a RQPA for a blended OPC cement obtained with the fly ash described in the previous paragraph. It was possible even to quantify the mullite content, in the cement. This number may be used to track down the approximate amount of fly ash added to the cement in the industry. Quartz is not a suitable compound to carry out this type of calculations as it may be present in the gypsum and/or in the additions like limestone, chert, etc. Hydration products RQPA has been employed for a number of applications related to the hydration reactions of OPC materials. The uses have been expanded from the hydration of model systems (for instance a single phase or an artificial mixture, Bellman et al. 2010) to blended cements and the role of admixtures and superplasticizers. It must be highlighted that the impact of admixtures on the hydration kinetics of Portland cement has been recently reviewed (Cheung et al. 2011) although that paper focused on the materials and not on the techniques to be used. RQPA was used to study the hydration reactions of commercial OPC in reflection geometry with laboratory data (Scrivener et al. 2004). The results were satisfactorily compared to those obtained from thermal analysis and electron microscopy. RQPA, using the internal standard approach in transmission geometry, was employed for studying OPC hydration products (Mitchell et al. 2006). The data obtained from capillary measurements showed little preferential orientation, and produced the progression of phase contents expected from the reaction. This study highlighted the benefits of the transmission geometry as more particles are measured which yields more reliable quantitative results. The early hydration of white Portland cement was also studied by in situ X-ray powder diffraction (reflection geometry) at defined temperatures and with different water/cement ratios (Hesse et al. 2008, 2009). The hydration of an OPC cement at 28 days was studied by RQPA using the external and internal standard methods including the role of isopropanol to stop the hydration reaction (Le Saout et al. 2007). Figure 7 displays the typical Rietveld plot for that material where the relevant peaks are labeled. RQPA based on in-situ synchrotron powder diffraction was used to monitor the evolution of hydrous phases during early hydration with a time resolution of 10 seconds (Weyer et al. 2005). A related work but with lower time resolution (minutes) studied the hydration process Table 4. Rietveld quantitative phase analysis (wt%) of a fly ash. Phase Fly ash + internal standard RQPA direct result Fly ash analysis Final result Mullite 9.5(2) 11.1(4) Hematite 3.9(2) 4.6(6) Quartz 7.4(2) 8.7(6) Wollastonite 0.8(2) 1.0(6) Corundum (WS = 47.7 wt%) (RS = ) 78.3(6) ----- ACn content#----- 74.6 # ACn stands for amorphous plus not-quantified crystalline phase(s) which includes misfitting problems and not-computed phase(s). 188 Aranda, De la Torre, León-Reina Fly ash + Al2O3(spiking method) Blended OPC cement Al2O3 Al2O3 Al2O3 Al2O3 Al2O3 Al2O3 Al2O3Al2O3 Quartz Quartz Quartz Mullite Mullite Quartz Gypsum Calcite Mullite Mullite Figure 6. (top) Full region of a Rietveld plot (CuKa1) for a fly ash mixed with Al2O3 as internal standard (47.7 wt%). The main peaks are labeled. (bottom) Full region of the Rietveld plot (CuKa1) for an industrial blended OPC obtained from that fly ash. The main diffraction peaks, which are not due to clinker phases, are highlighted. Fly ash + Al2O3(spiking method) Blended OPC cement Al2O3 Al2O3 Al2O3 Al2O3 Al2O3 Al2O3 Al2O3Al2O3 Quartz Quartz Quartz Mullite Mullite Quartz Gypsum Calcite Mullite Mullite Rietveld Quantitative Phase Analysis of OPC 189 on synthetic clinker phases (C3A and C4AF) and on commercial OPC cements (Merlini et al. 2007a,b). Furthermore, synchrotron powder diffraction was also used to monitor the evolution of ettringite in C3A-gypsum synthetic mixture and in commercial OPC cement systems during the first hours of the hydration process (Merlini et al. 2008). In-situ synchrotron RQPA was also carried out for studying the very early hydration of Class A and H oil well Portland cements with different amounts of CaCl2 at 25 and 50 °C (Jupe et al. 2007). On the other hand, synchrotron radiation may be used in more sophisticated types of characterization. For instance, high-energy synchrotron X-ray microdiffraction was used to quantify the orientation distribution of ettringite crystals. Diffraction images were analyzed using the Rietveld method to obtain information on textures within thin slabs of mortars (Wenk et al. 2009). The hydration reactions of an alkali-poor and an alkali-rich OPC were followed by RQPA. Significant differences during the early hydration were measured due to the presence of syngenite, K2Ca(SO4)2·H2O, when the alkali content is high and secondary gypsum when the alkali content is low. Furthermore, the pore solutions of the hydrated cements were analyzed and superor undersaturations for relevant minerals were calculated (Stark et al. 2008). In situ X-ray diffraction for monitoring cement hydration was used to study well defined Portland cement clinkers consisting of alite and aluminate doped with different amounts of Na2O. Other techniques such as isothermal conduction calorimetry and differential scanning calorimetry, scanning electron microscopy and 27Al NMR technique were also used (Wistuba et al. 2007). Finally, flash setting accelerators (both alkali-rich and alkali-free) are a class of admixtures commonly used for sprayed concrete during tunnel excavation. RQPA was also used to studying the setting behavior in this special application (Maltese et al. 2007). RQPA has been used in many works to study the hydration reactions of blended cements. Initially, this technique was used to analyze the hydration progress of cement pastes prepared by adding BFS and limestone powder (Hoshino et al. 2006). Selective dissolution was also employed to distinguish between the amorphous contents coming from BFS and newly-formed CH CSH2 CH Figure 7. Rietveld plot (CuKa1,2) for a 28 days hydrated OPC cement. The upper right inset shows the influence of isopropanol for the cement hydrated at 28 days (modified after Le Saout et al. 2007). 190 Aranda, De la Torre, León-Reina CSH gel (the amorphous Calcium-Silicate-Hydrated gel formed in the hydration of the calcium silicates). It was concluded that BFS accelerates the hydration of C3S, C3A and especially C4AF. The early age hydration and pozzolanic reaction in natural zeolite blended Portland cements has been studied by in situ synchrotron RQPA to determine the reaction kinetics and products (Snellings et al. 2010). A deep study was also carried out to quantitatively explain the effect of water curing condition on compressive strengths of fly ash cement pastes (Termkhajornkit et al. 2006). Replacement ratios of fly ash were 0%, 25% and 50% of total powders and the water to binder ratio was relatively low, 0.80 and 1.00 by volume. The time evolution of every OPC initial phase was worked out by RQPA. Unfortunately, the time evolution of portlandite was not quantitatively reported in that paper. The hydration degree of belite was the most affected parameter by the fly ash. On the other hand, a very recent and complete study used RQPA, together with thermogravimetry, scanning electron microscopy and isothermal calorimetry, in order to understand the hydration mechanisms of blended Portland cements containing fly ash and limestone powder (De Weerdt et al. 2011). In addition, pore solution analysis and thermodynamic modeling techniques were also employed. The time-evolution of all phases during hydration were studied (including portlandite from TGA and RQPA), and not only the pozzolanic effect was studied, but the variations in chemical shrinkages were also understood. Furthermore, the effect of fly ash on the kinetics of Portland cement hydration at different curing temperatures has also been investigated by RQPA (Narmluk and Nawa 2011). The hydration reactions of OPC were quantified by RQPA and the overall degree of fly ash hydration was determined from a selective dissolution method. Ternary binders composed of OPC, calcium sulfoaluminate clinker (CSA) and anhydrite were examined in order to study the impact of variations of the OPC:CSA:CS ratio on the hydration process and related mortar properties. RQPA was used to determine the mineralogical composition of the starting cementitious materials. Thermodynamic modeling was used to establish the phase assemblage which was also studied by calorimetry, DTA-TGA, SEM and X-ray powder diffraction for phase identification (Pelletier et al. 2010). RQPA and thermal methods were used to determine the phase development up to 28 days of hydration in normal and ultra-high performance cementitious systems (UHPC) that contains silica fume and fly ash (Korpa et al. 2009). For the calculation of the ACn content, the vacuum dried powdered specimens were mixed with ZnO as internal standard. For both formulations the most remarkable changes of the phase contents were measured in the first few days of hydration. To finish this section we would like to highlight that many hydrated phases may be present in a given hydrated/hydrating sample. Figure 8 displays the Rietveld plot of a sample showing one of the richest phase assemblage found in our laboratory. The peaks are labeled to easily identify each crystalline phases. The crystalline phases of this hydrated cement are mainly arising from the calcium sulfoaluminate cement fraction but we choose this sample to illustrate the amount of phases that can coexist in a paste (Fig. 8, Table 3). Durability studies Rietveld quantitative phase analysis may also help to understand/characterize the durability of the resulting mortars and concrete. Deterioration of cementitious building materials is often caused by sulfate attack at moderate temperatures due to delayed ettringite formation. Hence, several studies addressed this issue using RQPA (Katsioti et al. 2011). For instance, four cements were used to address the effect of tricalcium silicate content on external sulfate attack in sodium sulfate solution (Shanahan and Zayed 2007). Durability was studied by using linear expansion and compressive strength. Phases associated with deterioration were examined using scanning electron microscopy and RQPA. The resistance to sulfate attack of mixtures accelerated with alkali-free and alkaline accelerators was also studied by a number of techniques including RQPA which enabled the quantification of ettringite and gypsum over time (Paglia et al. 2003). On the other hand, thaumasite is mostly observed at low temperatures Rietveld Quantitative Phase Analysis of OPC 191 (usually lower than 15 °C). Hence, the effect of ettringite on thaumasite formation was studied in synthetic OPC materials using this methodology (Kholer et al. 2006). It must be highlighted that ettringite and thaumasite form a solid solution that has been extensively studied (Barnett et al. 2002; Torres et al. 2004). Another durability concern in OPC concretes is the alkali-aggregate/alkali-silica reaction (see for instance: Thomas et al. 2006; and references therein). Some aggregates, mainly silica but also carbonate, may provoke the expansion with failure of OPC concretes. RQPA has been employed to study the aggregates with the final aim to understand these reactions (Grattan-Bellew et al. 2010). Furthermore, this technique has also been employed, plus other characterization tools, to study the alkali-aggregate reaction in OPC and waterglass-alkaliactivated slag mortars (Puertas et al. 2009). Finally, composition and microstructure changes of cement pastes under a heating and cooling cycle were monitored by neutron powder diffraction. The parameters involved in the study were the heating ramp, the state of the sample (in block or ground) and the type of cement. Unfortunately, the Rietveld method was not applied to quantify the phases in the mixtures (Castellote et al. 2004). Neutron powder diffraction was subsequently used for studying the phase composition changes of cement pastes during accelerated carbonation experiments (Castellote et al. 2008). Selective dissolution Selective dissolution may be applied to OPC clinkers (or cements) or to blended cements with different methodologies (Gutteridge 1979; Luke and Glasser 1987). For OPC clinkers, both aluminates and silicates residues can be obtained. This is very useful for ensuring the polymorph present in the samples as the enriched phase may be identified much more easily. On the other hand, selective dissolution of blended cements is also used to determine the hydration degree of the addition (for instance fly ash or blast furnace slag). In these cases, AFt CSH 0.5 AH 3 CC C 3 AH 6 AFt AFt AFt AFt C 3 AH 6 C 3 AH 6 C 3 AH 6 C 3 AH 6 C 3 AH 6 AH 3 CSH 0.5 CSH 0.5 CSH 0.5 AFm-C AFm-C AFm-C AFm-C AFm-C katoite katoite Figure 8. Rietveld plot (CuKa1) of a fully hydrated blended cement paste mainly composed of calcium sulfoaluminate cement. The main crystalline peaks are labeled. 192 Aranda, De la Torre, León-Reina special selective dissolution methodologies have been developed (see for instance Ben-Haha et al. 2010). In 2003, Lundgaard and Jons described the application of RQPA to the aluminate residues of grey Portland clinkers. Several NIST reference clinkers were analyzed. The salicylic acid/ methanol extraction method (SAM) was used to dissolve silicate phases (alite, belite) and free lime. So, the minor content phases, aluminate, ferrite and sulfates were enriched. Furthermore, residues obtained from the chemical treatment of three NIST reference materials RM8486, RM8487 and RM8488 were analyzed by SEM and RQPA. The main finding was that chemical treatment was not fully selective/quantitative (Pritula et al. 2004b). So, this methodology is appropriate for enriching the low content phases. However, selective dissolution and RQPA of the residues does not directly improve the accuracy of the analytical results. On the other hand, special selective dissolutions for studying the hydration of blended cements have already been discussed above (Hoshino et al. 2006; Termkhajornkit et al. 2006; Brunet et al. 2010). INTERCOMPARISON AND COMPARISON WITH OTHER METHODS Before comparing the results of RQPA of cements with other techniques for quantitative mineralogical analyses, RQPA results of different laboratories should be compared. We highlight that this is possible for clinkers and cements but not for pastes as the evolving/ unstable nature of the samples do not allow to easily carry out an inter-laboratory study. Round robin (inter-laboratory) studies of RQPA were initially carried out for several types of samples but not OPCs (Toraya et al. 1999; Madsen et al. 2001; Scarlett et al. 2002). More recently, a partial round robin on RQPA of cement samples was published (Stutzman 2005; Stutzman and Leigh 2007). Unfortunately, the accuracy and uncertainty of the OPCs RQPA were not tested. Four cement reference specimens were prepared using NIST SRM clinkers compounded with known amounts of gypsum, bassanite, anhydrite, and/or calcite. The results of this study were used to estimate the interand intra-laboratory precision and bias of phase abundance determinations. Values of repeatability and reproducibility were given, but the statistical study was only based on the precision of the measurements/analyses. To evaluate the accuracy of the results, the use of these samples is not fully adequate since the “true” mineralogical compositions were not known. In a later study (Leon-Reina et al. 2009), a round-robin was conducted with two sets of samples, artificial mixtures and commercial OPCs. Artificial mixtures were prepared by mixing (weighing) synthesized single-crystalline phases in the appropriate proportions. These two samples were used to assess the accuracy and uncertainty of the procedure, as an expected mineralogical phase fraction—the “true mineralogical percentage”—is available under the assumption of negligible ACn contents. For a level of confidence of 95%, the general uncertainties were in the range 4.1-6.5% for C3S, 2.8-5.5% for C2S, 0.9-2.5% for C3A, 1.3-2.4% for C4AF, 1.0-1.6% for gypsum and 1.5-3.8% for calcite. The obtained precision values were much better. On the other hand, comparison of RQPA results can be carried out, with due care, with other analytical techniques. For clinkers and cements, point-counting microscopy techniques (optical and electronic) also directly measure the phase contents. In addition to these techniques, XRF directly measures the elemental compositions and, under some assumptions, a potential phase content can be established. For pastes, scanning electron microscopy, coupled to EDX microanalysis, is being utilized. However, a much straight forward method is the thermal decompositions, with their associated weight losses, as the decomposition temperature range may indicate the phase and the associate weight loss may allow measuring Rietveld Quantitative Phase Analysis of OPC 193 its content. Furthermore, other techniques such as calorimetry and nuclear magnetic resonance spectroscopy are emerging as quantitative tools. All these techniques are briefly reviewed next. Bogue and reverse Bogue calculation The most widely used method for estimating the potential phase composition of OPCs from the oxide analysis was developed long time ago (Bogue 1929; Taylor 1989) and generalized by the routine use of XRF analysis. An extensive work in this topic has been very recently reported/discussed (Le Saout et al. 2011) showing the associated errors to this methodology, so it is not further discussed here. We only want to highlight an excellent work (Crumbie et al. 2006) that employed four analytical techniques: RQPA, Bogue, optical microscopy and scanning electron microscopy coupled with energy dispersive spectroscopy (SEM-EDS); for the quantitative study of eight clinkers. That paper shows that the use of standard Bogue calculation to predict the phase composition of Portland clinkers can give serious errors. Optical and scanning electron microscopies After the appropriate sample treatment, optical microscopy coupled with point counting techniques can produce very reliable phase quantification especially for the silicate phases, alite and belite (Campbell and Galehouse 1991; Taylor 1997; Campbell 1999; Fullmann and Walenta 2003). However, the quantification of the aluminate and the ferrite phases is often quite difficult, due to the very small crystal size of these interstitial phases. Furthermore, the different crystallographic forms of C3A (cubic, orthorhombic) cannot be differentiated (Walenta and Fullmann 2004). There is no need to emphasize that sample preparation, data acquisition, and data analysis are more demanding than for RQPA. It must be mentioned that the International Cement Microscopy Association http://www.cemmicro.org/ which began in 1981, develops several activities including the organization of annual meetings. The published proceedings serve as a working tool and source of informative references in the areas of clinker, cement, concrete, and other building materials. On the other hand, SEM-EDS studies are carried out to quantify the chemical (elemental) composition of selected phases within OPCs (see for instance: Gobbo et al. 2004; Crumbie et al. 2006). Both optical and electron microscopies are good complementary techniques to RQPA of clinkers and cements (Campbell and Galehouse 1991; Stutzman and Leigh 2002; Suherman et al. 2002; Stutzman 2011 and references therein). Other electron microscopy studies can be carried out. For instance, high-resolution cold field emission-scanning electron microscopy, in addition to isothermal conduction calorimetry and RQPA of the initial cements, was used to understand the end of the induction period of OPCs (Makar and Chan 2008). Finally, it should be kept in mind that microscopy techniques directly give volume fractions but Rietveld software usually gives weight fractions. The comparison is straightforward for anhydrous cements by using the crystallographic densities (already within the software calculations) to renormalize one of the results. However, this comparison is not straightforward for hydrating samples as the densities of some (amorphous) hydrates are not well known. The volume variation during hydration is necessary for understanding chemical shrinkages of pastes, mortars and concretes. Thermodynamic modeling In this approach, the calculated hydration rates of the individual clinker phases are used as the (time-dependent) input under the relevant conditions once the appropriate database is developed (Matschei et al. 2007b). The modeled data can be compared with the measured composition of pore solutions as well as with any experimental quantitative phase analysis technique (Lothenbach and Winnefeld 2006). This approach was extended to variabletemperature hydration studies (Lothenbach et al. 2008a) and it has been very recently reviewed (Damidot et al. 2011). 200 Aranda, De la Torre, León-Reina optimized coefficients were 0.855(3) and 0.961(2) for the Cu-Ka1 and Mo-Ka1,2 patterns, respectively. However, the resolution of the Mo-pattern is not very good (see inset of Fig. 9, bottom) and better equipment is expected in the near future, including the key development of a primary monochromator for laboratory Mo-Ka radiation. A second approach is to increase the accuracy of the RQPA results by combining at least two data sets. For instance, it is possible to carry out a RQPA for a single sample but from two data sets, e.g., one high-resolution powder data collected in reflection and a second pattern collected in transmission in order to have a better powder averaging although the resolution of the diffraction peaks may be lower. Figure 10 shows the Rietveld fits of calcium y 2-Theta, deg Counts 10.0 20.0 30.0 40.0 50.0 60.0 70.0 X10E4 0.0 1.0 2.0 3.0 4.0 2-Theta, deg Counts 10.0 20.0 30.0 40.0 50.0 60.0 70.0 X10E3 0.0 1.0 2.0 y 2-Theta, deg Counts 10.0 20.0 30.0 40.0 50.0 60.0 70.0 X10E4 0.0 1.0 2.0 3.0 4.0 2-Theta, deg Counts 10.0 20.0 30.0 40.0 50.0 60.0 70.0 X10E3 0.0 1.0 2.0 y 2-Theta, deg Counts 10.0 15.0 20.0 25.0 30.0 35.0 X10E4 0.0 0.5 1.0 1.5 2.0 y 2-Theta, deg Counts 10.0 15.0 20.0 25.0 30.0 35.0 X10E3 0.0 1.0 2.0 CuK1 Reflection CuK1,2 Transmission CSH2 CSH2 Figure 10. (top) Full region of a Rietveld plot of high-resolution CuKa1 laboratory data collected in reflection geometry for a calcium sulfoaluminate cement containing nine crystalline phases. (bottom) Full region of a Rietveld plot of medium-resolution CuKa1,2 laboratory data collected in transmission geometry for the same calcium sulfoaluminate. The insets show enlarged views of the low-angle regions to highlight the effects of the gypsum preferred orientation. Rietveld Quantitative Phase Analysis of OPC 201 sulfoaluminate cement where the phase analysis has been carried out fitting simultaneously a high resolution pattern collected in reflection and a medium-resolution pattern collected in transmission. We must highlight that both fits are carried out with a final gypsum optimized content of 13.5(1) wt% but the March-Dollase preferred orientation correction coefficients were 0.499(8) and 1.37(2) for the reflection and transmission patterns, respectively. This cement has a very complex phase assemblage formed by: cubic-Yeelimite, Ca4Al6O12SO4, 23.6(2) wt%; orthorhombic-Yeelimite, 15.9(2) wt%; ternesite, Ca5(SiO4)2SO4, 16.7(3) wt%; gypsum, 13.5(1) wt%; b-belite, 9.9(1) wt%; anhydrite-II, 8.3(1) wt%; alite-M3, 6.1(1) wt%; calcium titanium perovkskite, CaTiO3, 4.7(1) wt%; and dolomite, (Mg,Ca)CO3, 1.2(1) wt%. 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